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Optimal Quantum Detection Strategies: Enhancing Information Extraction Without Disturbance

This paper explores optimal detection strategies in quantum systems, specifically focusing on composite systems without nonlocal properties. Chih-Lung Chou and Li-Yi Hsu highlight how combined measurements can significantly improve information extraction from quantum states, increasing average information gain from 1.05228 bits in separate measurements to 1.36907 bits when combined. The study also addresses the challenges of measurement disturbance in quantum states, particularly when inferring the state of signal qubits through direct detection. Strategies for optimizing detection probability are proposed.

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Optimal Quantum Detection Strategies: Enhancing Information Extraction Without Disturbance

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  1. Optimal Quantum Detection without Disturbance Chih-Lung Chou, CYCU & Li-Yi Hsu, NCTS

  2. Instead of considering composite quantum systems that consists of non-interacting parts, A. Peres and W. K. Wootters discussed a particular composite quantum system that possesses no nonlocal properties. PRL66, 1119(1991) For instance,

  3. They found that the information can be better extracted by doing combined measurements. and likewise define and , by cyclic permutations. i.e., the measurementM can be chosen as:

  4. As a result, the average information gain increases from 1.05228 bit(by separate measurements) to 1.36907 bit(by combined measurements) Combined measurementsWIN!

  5. However, measurements on the signal states will unavoidably destroy the states at the same time.

  6. X Z o o o 120 120 120 Spin-up in z direction : the signal qubit

  7. e.g., By performing measurements on , we can infer the state of the signal qubit .

  8. Measuring direction Probability of success detection If we detect the signal qubit directly, the optimal probability for Stern-Gerlach measurements is

  9. Separate measurements on

  10. Combined measurements on define Orthonormal basis

  11. Detection strategy (1) (2) If the outcome is f4, make a random guess for the signal qubit. Result:

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